Let a be the first term and d be the common difference, then the sides of triangle are a, a + d and a + 2d.
Area of triangle = 1/2 x Base x Height
Substituting the values, we get
a(a + d) = 2 x 24
a(a + d) = 48 ....(1)
Applying Pythagoras theorem, we get
From Eq. (1), we know that a + d ≠ 0. Therefore,
3d - a = 0 ⇒ 3d = a
Substituting in Eq. (1), we get
3d(3d + d) = 48
⇒ 3d x 4d = 48
⇒ d2 = 48/12 ⇒ d2 = 4 ⇒ d = 2
From 3d = a, we get
a = 2 x 3 = 6 ⇒ a = 6
Therefore, the sides of the triangle are 6, (6 + 2), (6 + 2 x 2), that is, 6, 8, 10.